How can I fix broken linked dupligroups when the source file/directory has changed?
This has been fixed in Blender 2.77

To fix broken dupligroup links when the path to the source file (directory name/s) has changed; (//directoryA/source.blend changed to //directoryB/source.blend):


Go to File/External Data
Select "Find Missing Data"
Navigate to the new location, click Find Missing Files
Save, then close and re-open file.


To fix a broken dupligroup link when the filename of the source .blend file has changed (//directoryA/oldName.blend changed to //directoryA/newName.blend) 


Go the Outliner
In the pulldown box that by default says "All Scenes" select "Data-Blocks"

Expand the "Libaries" section
Expand the "Lib" section for whichever linked Dupligroup you're fixing

In the "File Path" field remove the old path/filename and type in the new path/filename. (it should start with // if you're using relative paths)

Save, then close and re-open file.


The last option will also work for changed file name and path; just manually type in the full new path and filename.

This was information given in the Blender 2.77 release notes. It says that "In case of missing libraries on load, empty placeholder datablocks get added, which allows to restore or relink." and in the Datablocks and Libraries Management section of the release notes it says that this allows the user to "Edit missing libs paths in the Outliner, save &amp; reload main .blend file, and get missing linked datablocks back."

Awesome! Thanks Blender developers! :)